A penny weighs 2.5 grams while a dime weighs about 2.27 grams. How much do a penny and two dimes weigh?
The Correct Answer and Explanation is:
To determine the total weight of a penny and two dimes, we begin by identifying the individual weights of each coin:
- A penny weighs 2.5 grams.
- A dime weighs 2.27 grams.
Since the question asks for the total weight of one penny and two dimes, we calculate the weight of the two dimes first: Weight of two dimes=2×2.27=4.54 grams\text{Weight of two dimes} = 2 \times 2.27 = 4.54 \text{ grams}Weight of two dimes=2×2.27=4.54 grams
Next, we add the weight of the penny to the total weight of the two dimes: Total weight=2.5+4.54=7.04 grams\text{Total weight} = 2.5 + 4.54 = 7.04 \text{ grams}Total weight=2.5+4.54=7.04 grams
Final Answer:
A penny and two dimes weigh 7.04 grams.
Textbook-Style Explanation:
Understanding how to combine weights is an essential application of basic arithmetic. When calculating total mass, especially in problems involving real-world objects like coins, it is important to use precise values and proper units.
In this example, we are given that a penny weighs 2.5 grams, and a dime weighs 2.27 grams. The question requires the total mass of one penny and two dimes. This means we need to find the combined mass of these three coins.
To do this, we multiply the weight of one dime by two because there are two dimes: 2.27 grams/dime×2=4.54 grams2.27 \text{ grams/dime} \times 2 = 4.54 \text{ grams}2.27 grams/dime×2=4.54 grams
We then add the weight of one penny to this total: 4.54 grams+2.5 grams=7.04 grams4.54 \text{ grams} + 2.5 \text{ grams} = 7.04 \text{ grams}4.54 grams+2.5 grams=7.04 grams
This demonstrates how addition and multiplication are used together to find the combined weight of multiple objects. It also emphasizes the importance of using accurate measurements and appropriate units. Such skills are widely applicable in both academic settings and daily life, such as when estimating postage, measuring ingredients, or managing inventory.
